If x+iy=`frac{a+ib}{a-ib}`, prove that `x^2`+`y^2` = 1

Similar Questions

Explore conceptually related problems

If x -iy = frac{a-ib}{c-id} , then prove that ( x^2 + y^2 ) = frac{a^2+b^2}{c^2+d^2}

If x-iy = sqrt (frac{a-ib}{c-id}) , prove that (x^2+y^2) = frac{a^2+b^2}{c^2+d^2}

If x +iy = (a + ib) / (a - ib) , prove that x^2 + y^2 = 1 .

If x+iy= sqrt (frac{a+ib}{c+id}) , Prove that, (x^2+y^2)^2 = frac{a^2+b^2}{c^2+d^2}

If x + iy = (a + ib)/(a - ib), prove that x ^(2) + y ^(2) =1.

If a+ib= frac{1+i}{1-i} , then prove that ( a^2 + b^2 )=1

If (a+ib) = frac{(x+i)^2}{2x^2+1} , prove that a^2 + b^2 = frac{(x^2+1)^2}{(2x^2+1)^2}

If a + ib = (1 + i) / (1 - i) , prove that a^2 + b^2 = 1

If x+iy= (a+ib)^3 , show that x/a+y/b=4( a^2 - b^2 )

If frac{a+3i}{2+ib} = 1-i, show that (5a-7b)=0